Particle swarm optimisation (PSO) is a metaheuristic algorithm used to find good solutions in a wide range of optimisation problems. The success of metaheuristic approaches is often dependent on the tuning of the control parameters. As the algorithm includes stochastic elements that effect the behaviour of the system, it may be studied using the framework of random dynamical systems (RDS). In PSO, the swarm dynamics are quasi-linear, which enables an analytical treatment of their stability. Our analysis shows that the region of stability extends beyond those predicted by earlier approximate approaches. Simulations provide empirical backing for our analysis and show that the best performance is achieved in the asymptotic case where the parameters are selected near the margin of instability predicted by the RDS approach.

中文翻译：

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粒子群优化算法的随机稳定性

粒子群优化（PSO）是一种元启发式算法，用于在各种优化问题中找到良好的解决方案。元启发式方法的成功通常取决于控制参数的调整。由于该算法包括影响系统行为的随机元素，因此可以使用随机动力学系统（RDS）的框架进行研究。在PSO中，群体动力学是准线性的，因此可以对其稳定性进行分析处理。我们的分析表明，稳定性范围超出了早期近似方法所预测的范围。仿真为我们的分析提供了经验支持，并表明在渐近情况下，在RDS方法预测的不稳定性裕度附近选择参数的情况下，可以获得最佳性能。